VOiL. 13, 1927
PHYSICS: C. BAR US
223
the liquid is not crystalline, but is one in which molecular mobility is
permitted and the resulting peaks represent the most probable spacings.
A name is proposed for this non-crystalline, space-array state. The
noun is cybotaxis and the adjective cybotactic.
This conception of the liquid state gives a description of a "solution"
and contributes to various theories in connection with liquids. The
experiments and discussion will soon be published in full.
1 Debye and Scherrer, Nachr. Gesell. Gottingen (1916), p. 6.
2
3
4
Vide Hewlett, Phys. Rev., 20 (1922), p. 688 and others.
Muller and Saville, Journal Chem. Soc., 127 (1925), p. 599.
Adam, Proc. of Roy. Soc. (1921), (1922), (1923).
PINHOLE PROBE MEASUREMENTS WITH MASSIVE
CYLINDRICAL AIR COL UMNS*
By CARI BARUS
DUPARTMINT OF PHYSICS, BROWN UNIVZRSITY
Communicated March 8, 1927
1. Introductory.-After completing the work with the broad horn of
my last paper,' similar experiments were made with a long slender horn
(40 cm. long) and with cylindrical tubes (28 cm. long, 2.8 cm. diam.).
The results in the former case are too complicated to be given here. In
the latter (tube), the nodal pressure-capacity (s, C) graphs of the transformer (electric oscillation) consisted of a group of nearly straight and
parallel lines, running close together, so long as the pinhole lay below
the middle (d = 14 cm.) of the tube. After this (d = 15 cm. to 0) the
slopes decreased rapidly. There were no marked crests, but rather noise
increasing continuously with the capacity, C, or falling pitch. The break
circuit (electric siren) graphs, however, showed the usual cuspidal crests
(here at a', e", a") with long intervals of relative silence between. As far
as the middle of the pipe, the crests were about of the same nodal intensity,
s. Hence these data accentuate the results already described for the horn.
In the s-d graphs, the a' and a" crests lay at about d = 7 cm. and near the
bottom, while the e" crest was marked near the middle d = 15 cm. of the
pipe. From this it appears both the a' and a" of the motor break (siren)
evoke the first overtone a" of the d' closed organ pipe; whereas in the case
of the e", the pipe with a telephone plate at one end vibrates as an open
organ pipe with a node near the middle.
2. Extensible Pipe.-Since there are three vibrating systems in the transformer method, two of them should be made adjustable if the third is
given, to obtain the largest acoustic pressure values (s). An extension
224
PHYSICS: C. BAR US
PROC. N. A. S.
was, therefore, added to the pipe (insert, figure 1) so that its length could be
increased continuously, from d = 28 to 35 cm. By setting this for the
maximum s at any capacity, C, the remainder of the curve was then worked
out. A remarkable result presented itself, with an important bearing on
the pinhole probe, inasmuch as the graphs now consisted of right line elements, between breaks.
In figure 1 the largest s was first found for the pipe depth near d = 30
cm. by tuning (the probe being at the bottom of the tube as usual). The
graph obtained for varying C (O to 1.1 m.f.) starts with a linear sweep
as far as C = 0.3 m.f. (a'), then bends abruptly to a second linear sweep
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as far as C = 0.9 m.f., after which the course is curved to the crest beyond
the figure. It would seem that each of these lines corresponds to a given
kind of vibration; i.e., to a given overtone which breaks abruptly into the
next available.
The behavior of the untuned pipe (d = 28 cm.) for the given spring
tension is shown in the lower curve. There is a break at C = 0.2 (d") and
at C 1.0 (c') m.f. In the repetition (black dots) the break at C = 0.7
(# d') is probably an accidental small change in the tension of the
electrical spring break. Between these points the graph is strikingly
linear.
After the tube was further elongated to the pipe depth, d = 35 cm.,
now adequately in resonance with the spring break, a second and much
VoL. 13, 1927
225
PHYSICS: C. BAR US
stronger maximum, figure 2, appeared. The rectilinear progress between
C = 0.1 to 0.3, 0.4 to 0.5, 0.6 to 0.8, 1.0 to 1.2, 1.3 to 1.5, 1.6 to 2.0 m.f.,
is marked throughout. Even near the crest C = 1.2 the tendency is still
observable. This relatively enormous crest (s = 475) is in keeping with
the near resonance of break, pipe and electric oscillation.
It seemed worthwhile to test the case further with untuned lengths between d = 28 cm. and d = 34 cm., and throughout large C ranges (0 to 2
m.f.). Examples of the graphs are given in figure 2 for an altered transformer spring tension. Broken rectilinear paths are the rule particularly
for d = 31, 33, where the roof-like crests are striking.
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Finally in figure 3 for the optimum d = 35, the successively tuned pipe
(open circles) is compared with the untuned pipe (black circles). Below
C = 0.5 the divergence is not large, both starting under tuned conditions.
Thereafter the divergence rapidly increases, the tuned pipe naturally being
in excess. From C = 0.8 on, passage of the untuned (n) condition to the
tuned condition (t) is indicated by arrows. To get the maximum svalues it is thus necessary to re-tune the pipe at all pitches. The successive tuning (resonance throughout) has raised the crest to nearly s
= 550, an acoustic pressure of over 0.4 mm. of Hg.
The same figure shows the corresponding behavior at the smaller maximum at d = 31. Linear progress is interrupted by the tuning indicated
by the arrows.
226
PHYSICS: C. BAR US
PROC. N. A. S.
3. Closed Organ Pipe.-The open-mouthed organ pipe is very noisy,
so that in this respect the doubly closed organ pipe shown in the insert,
figure 4, is preferable. Here p is the pipe 27 cm. long in the clear, T the
attached activating telephone and bc the pinhole probe. The point c
may either be thrust to the rear, near the telephone, or (as in figure)
the pinhole c may be near the front of the tube. This should make no
difference in the acoustic pressure, s, other things being equal. The telephone, T, was activated by the transformer method, as the specific results
of this method are particularly in question.
The graphs R and F (the former raised for clearness), for the same tense
spring break adjustment left unchanged, but with the pinhole, respectively,
in the rear (bottom) and in the front of the doubly closed tube, are practically identical. They again consist of linear parts (as above) with abrupt
breaks. Each exhibits two crests, respectively, above a' and # d'.
4. Alternating Current.-The attempt to energize the primary of the
induction coil by an alternating current proved unsatisfactory for the
reason that while the induction is relatively feeble as compared with the
break circuit methods used heretofore, the heating effect of these continuous currents is out of all proportion.
5. Remarks.-In my work heretofore, I have associated the fringe displacement, s, i.e., the nodal intensity or acoustic pressure with the
usual energy (E per unit of volume) equation. If n is the frequency and a
the amplitude of the sound wave, we may, therefore, write E = p + pv2/2
- Ks + (p/2) (27ran)2. At the mouth of the tube s is zero and a the
maximum; at the bottom or node a is zero and s a maximum. The expectation that a similar equation could also be used to interpret the fringe
displacement at a given point for different frequencies is not warranted.
For if we put 47r2n2 = 1/LC,p = Ks and assume E to be constant along the
linear elements of the graphs, the result is - (s -s') = (p/2KL) (A 2/CA '2/C') whereas the graphs suggest As cc AC simply, along each element.
The view that the oscillation frequency (n) of the organ pipe is impressed
on the oscillation frequency (n') of the secondary actuating the telephone
plate is also unsatisfactory. For if Y is the amplitude of the electric
circuit under a harmonic electromotive force E cos cot
Y=
E/V(C,o'2_-2)2 + K2wO2
where to = 2wn and co' = 27rn' are the angular frequencies of the free and
frictionless acoustic and electrical circuits, respectively, and K is the
coefficient of friction. This may as usual be reduced to proportionalities
in the form y = 1/V(1-x2)2 + a2x2 where x = cco', a = Klco
y = Y/(E/w'2). This y has a crest for x2 = 1-Ya2/2.
If co' = 1/LC and K is relatively very small, the equation reduces to
Voi. 13, 1927
227
PHYSICS: J. K. MORSE
ELC(1
1-02LC \
KwLC \2
-@2c
approximately, where co, K, L are constant and C variable. Hence, even
if we neglect the term in K and associate Y with the fringe displacement, s,
an equation in this form is not serviceable in identifying As c AC along
linear elements, unless w2LC is small compared with 1. This would not be
the case with the fundamental or any harmonics of the cylindrical pipe.
Even if X refers to the frequency of the spring break taken at pitch a,
the equation remains inapplicable.
This suggests a simpler approach through the capacity equation Q =
CV whence As cc Ai = (d V/dt) AC; or the slopes of the linear elements of
the graphs are to be associated with the effective time rate at which the
potential of the condenser changes. The value of d V/dt depends on the
form of residual wave on which the new impulse is superimposed. Moreover a reason for the broken linear relations of s and C is now apparent;
for the fringe displacement s measures the difference of level of the surfaces
of mercury in the U-gage. It, therefore, also measures the potential energy
localized in the stationary wave at the point of the pinhole probe, though
it does this with a coefficient which may be either positive or negative.
The stream lines run from the outside to the inside of the pinhole embouchure.
* Advance note from a Report to the Carnegie Inst. of Washington, D. C.
'These PROCZZDINGS, 13, pp. 52-56, 1927.
ATOMIC LATTICES AND ATOMIC DIMENSIONS
By JARBD KIRTLAND MORSB'
DZPARTMUNT
OF PHYSICS,
UNIVzRSITY Or
CHICAGO
Communicated March 4, 1927
By means of the concept of a spherical atom W. L. Bragg2 and W. P.
Davey3 have independently computed the radii of atomic spheres of influence from the distances of closest approach obtained from X-ray measurements on crystals. In this paper these spherical atoms are specialized
and the cubic atom proposed by Lewis and developed by Langmuir is
extended to simple polyhedrons inscribable in spheres. It is shown in
detail how these simple models can be built up into various types of observed cubic and hexagonal lattices and how the lattice constants are
geometrically related to the atomic radii. From these relations possible
atomic radii are computed and tabulated.